Learning Analysis
Adani B. Abutto
2025-06-06
1 Data Import and Cleaning
1.1 Stimuli
# import stimuli information
df.stimuli =
read_csv(paste0(data_dir,
"fun-puzzles-exp1/production2_puzzles-test.csv"))
df.stimuli %>%
head()## # A tibble: 6 × 15
## puzzle_id collection_name level_name layout level_width level_height
## <dbl> <chr> <dbl> <chr> <dbl> <dbl>
## 1 0 Microban 67 ['###… 7 8
## 2 1 Microban 33 ['###… 7 7
## 3 2 Microban 26 [' ##… 6 8
## 4 3 Sokogen-990602… 13 ['###… 8 6
## 5 4 Sokogen-990602… 19 ['###… 6 6
## 6 5 Sokogen-990602… 41 ['###… 9 7
## # ℹ 9 more variables: sokobanonline__likes_rate <dbl>,
## # sokobanonline__solve_rate <dbl>,
## # sokobanonline__shortest_solution <dbl>, enjoyment_cat <chr>,
## # difficulty_cat <chr>, shortestPath_cat <chr>, stimuli_set <chr>,
## # boxes <chr>, start_position <chr>1.2 Metadata
## # A tibble: 6 × 20
## puzzle_id collection_name level_name layout level_width level_height
## <dbl> <chr> <dbl> <chr> <dbl> <dbl>
## 1 0 Microban 67 ['###… 7 8
## 2 1 Microban 33 ['###… 7 7
## 3 2 Microban 26 [' ##… 6 8
## 4 3 Sokogen-990602… 13 ['###… 8 6
## 5 4 Sokogen-990602… 19 ['###… 6 6
## 6 5 Sokogen-990602… 41 ['###… 9 7
## # ℹ 14 more variables: sokobanonline__likes_rate <dbl>,
## # sokobanonline__solve_rate <dbl>,
## # sokobanonline__shortest_solution <dbl>, enjoyment_cat <chr>,
## # difficulty_cat <chr>, shortestpath_cat <chr>, stimuli_set <chr>,
## # boxes <chr>, start_position <chr>, shortest_solution <dbl>,
## # astar_solution <chr>, astar_iters <dbl>,
## # astar_solution_length <dbl>, astar_solution_string <chr>1.3 Exclusions
df.exclusions =
read_csv(paste0(data_dir,
"fun-puzzles-exp1/production2_exclusions.csv"))
df.exclusions %>%
count(reasons)## # A tibble: 10 × 2
## reasons n
## <chr> <int>
## 1 Failed comprehension 2
## 2 Only 1 practice trials 1
## 3 Only 2 practice trials 5
## 4 bad trace log 38
## 5 comparison: only 7 posttest trials 2
## 6 comparison: only 7 pretest trials 4
## 7 empty trace log 12
## 8 test attempts: only 7 trials with trace data 6
## 9 test ratings: only 6 trials 1
## 10 test ratings: only 7 trials 151.4 Exit Survey Data
df.survey =
read_csv(paste0(data_dir,
"fun-puzzles-exp1/production2_survey.csv"))
df.survey_processed =
df.survey %>%
# mutate scales to show labels
mutate(judgedDifficulty = factor(judgedDifficulty,
levels = c(1, 2, 3, 4, 5),
labels = c("1\nVery Easy", "2", "3", "4", "5\nVery Hard")),
participantEffort = factor(participantEffort,
levels = c(1, 2, 3, 4, 5),
labels = c("1\nVery Low", "2", "3", "4", "5\nVery High")),
sokobanFamiliarity = factor(sokobanFamiliarity,
levels = c(0, 1, 2, 3),
labels = c("Never", "A few times", "Several times", "Very familiar")),
gamingFrequency = factor(gamingFrequency,
levels = c(0, 1, 2, 3, 4),
labels = c("None", "< 1h", "1-5h", "6-10h", "> 10h"))) %>%
# filter out exclusions
filter(!gameID %in% df.exclusions$gameID)
df.survey_processed %>%
head()## # A tibble: 6 × 27
## project experiment iteration stim_id gameID condition
## <chr> <chr> <chr> <chr> <chr> <chr>
## 1 fun-puzzles fun-puzzles-exp1 production2 6790956f9… 3940-… difficult
## 2 fun-puzzles fun-puzzles-exp1 production2 6790956f9… 7209-… difficult
## 3 fun-puzzles fun-puzzles-exp1 production2 6790956f9… 4733-… difficult
## 4 fun-puzzles fun-puzzles-exp1 production2 6790956f9… 6110-… difficult
## 5 fun-puzzles fun-puzzles-exp1 production2 6790956f9… 0047-… difficult
## 6 fun-puzzles fun-puzzles-exp1 production2 6790956f9… 2839-… difficult
## # ℹ 21 more variables: startInstructionTS <dbl>,
## # startPracticeTS <dbl>, startPreTS <dbl>, startMainTS <dbl>,
## # startPostTS <dbl>, startSurveyTS <dbl>,
## # startComprehensionTS <dbl>, endExperimentTS <dbl>,
## # participantExplanations <chr>, judgedDifficulty <fct>,
## # participantEffort <fct>, sokobanFamiliarity <fct>,
## # gamingFrequency <fct>, participantYears <dbl>, …1.5 Gameplay Data
8 test trials:
df.game =
read_csv(paste0(data_dir,
"/fun-puzzles-exp1/production2_testTrials.csv"))
df.game_processed =
df.game %>%
# filter out exclusions
filter(!gameID %in% df.exclusions$gameID) %>%
# complement puzzle ids
mutate(puzzle_id = paste(str_sub(collection_name, 1, 7), level_name)) %>%
# rename cols
rename(rating = rate_response,
ratingRT = rate_rt)
df.game_processed %>%
head()## # A tibble: 6 × 32
## project experiment iteration stim_id gameID condition study_phase
## <chr> <chr> <chr> <chr> <chr> <chr> <chr>
## 1 fun-puzzl… fun-puzzl… producti… 679095… 3940-… difficult test
## 2 fun-puzzl… fun-puzzl… producti… 679095… 3940-… difficult test
## 3 fun-puzzl… fun-puzzl… producti… 679095… 3940-… difficult test
## 4 fun-puzzl… fun-puzzl… producti… 679095… 3940-… difficult test
## 5 fun-puzzl… fun-puzzl… producti… 679095… 3940-… difficult test
## 6 fun-puzzl… fun-puzzl… producti… 679095… 3940-… difficult test
## # ℹ 25 more variables: trialNum <dbl>, stimuli_set <chr>,
## # author_name <chr>, collection_name <chr>, level_name <dbl>,
## # width <dbl>, height <dbl>, layout <chr>, boxes <chr>,
## # start_position.x <dbl>, start_position.y <dbl>,
## # select_response <dbl>, select_rt <dbl>, rating <dbl>,
## # ratingRT <dbl>, solveDuration <dbl>, solved <dbl>,
## # boxesSolved <dbl>, attempt_nInputEvents <dbl>, …# calculate summary ratings
df.summary_ratings =
df.game_processed %>%
# bootstrap ci
group_by(stimuli_set, puzzle_id, condition) %>%
tidyboot_mean(rating, na.rm = T) %>%
ungroup() %>%
# median, sd, etc.
left_join(summarizer(df.game_processed, target_cols = c(rating),
puzzle_id, condition) %>%
dplyr::select(-ends_with('mean')),
by = c("puzzle_id", "condition")) %>%
rename(rating_meanBoot = empirical_stat,
rating_mean = mean,
rating_ciLo = ci_lower,
rating_ciHi = ci_upper)
df.summary_ratings %>%
head()## # A tibble: 6 × 10
## stimuli_set puzzle_id condition n rating_meanBoot rating_ciLo
## <chr> <chr> <chr> <int> <dbl> <dbl>
## 1 A Microba 104 difficult 36 9.08 8.51
## 2 A Microba 104 enjoyable 32 4.28 3.41
## 3 A Microba 67 difficult 36 8.67 8
## 4 A Microba 67 enjoyable 32 4.03 3.23
## 5 A Sokogen 13 difficult 36 7.25 6.29
## 6 A Sokogen 13 enjoyable 32 5.59 4.57
## # ℹ 4 more variables: rating_mean <dbl>, rating_ciHi <dbl>,
## # rating_median <dbl>, rating_sd <dbl># add avg ratings to game data df
df.game_processed =
df.game_processed %>%
left_join(df.summary_ratings %>%
dplyr::select(condition, puzzle_id, rating_mean) %>%
pivot_wider(names_from = condition, values_from = rating_mean)) %>%
rename(mean_difficult = difficult,
mean_enjoyable = enjoyable) %>%
mutate(puzzle_id_sorted = reorder(puzzle_id, mean_difficult))16 comparison trials:
df.comparison =
read_csv(paste0(data_dir,
"fun-puzzles-exp1/production2_compareTrials.csv"))
df.comparison_processed =
df.comparison %>%
# filter out exclustions
filter(!gameID %in% df.exclusions$gameID) %>%
# keep only relevant cols
dplyr::select(gameID:level_name_1) %>%
# add phase and puzzle info
mutate(study_phase = factor(study_phase,
levels = c("pretest", "posttest")),
puzzle_id_0 = paste(str_sub(collection_name_0, 1, 7),
level_name_0),
puzzle_id_1 = paste(str_sub(collection_name_1, 1, 7),
level_name_1)) %>%
# keep only relevant cols
dplyr::select(-c(collection_name_0:level_name_1)) %>%
# compute response times
mutate(rt_done2 = rt_done2 - rt_done1,
rt_choose = rt - rt_done2)
df.comparison_processed %>%
head()## # A tibble: 6 × 13
## gameID condition stim_id study_phase trial_type trialNum response
## <chr> <chr> <chr> <fct> <chr> <dbl> <dbl>
## 1 3940-a6a… difficult 679095… pretest sokoban-c… 1 0
## 2 3940-a6a… difficult 679095… pretest sokoban-c… 2 0
## 3 3940-a6a… difficult 679095… pretest sokoban-c… 3 1
## 4 3940-a6a… difficult 679095… pretest sokoban-c… 4 0
## 5 3940-a6a… difficult 679095… pretest sokoban-c… 5 0
## 6 3940-a6a… difficult 679095… pretest sokoban-c… 6 1
## # ℹ 6 more variables: rt <dbl>, rt_done1 <dbl>, rt_done2 <dbl>,
## # puzzle_id_0 <chr>, puzzle_id_1 <chr>, rt_choose <dbl>Create dataset containing all relevant information at once:
df.analysis =
df.game_processed %>%
left_join(df.survey_processed %>%
dplyr::select(gameID,
judgedDifficulty,
participantEffort,
sokobanFamiliarity),
by = "gameID") %>%
left_join(df.metadata %>%
dplyr::select(puzzle_id_num = puzzle_id,
layout,
sokobanonline__solve_rate,
astar_iters, astar_solution_length),
by = "layout") %>%
left_join(df.survey_processed %>%
dplyr::select(gameID,
age = participantYears,
gender = participantGender),
by = "gameID") %>%
mutate(judgedDifficulty = as.numeric(judgedDifficulty),
sokobanFamiliarity = as.numeric(sokobanFamiliarity),
participantEffort = as.numeric(participantEffort)) %>%
dplyr::select(subject_id = gameID,
age, gender,
puzzle_id_sorted, puzzle_id_num,
trialNum, stimuli_set,
layout,
select_response, rating,
solveDuration, solved, boxesSolved,
attempt_nInputEvents, attempt_nRestart, attempt_nUndo,
sokobanonline__solve_rate, astar_iters, astar_solution_length,
judgedDifficulty, mean_difficult,
participantEffort, mean_enjoyable,
sokobanFamiliarity)
df.analysis %>%
head()## # A tibble: 6 × 24
## subject_id age gender puzzle_id_sorted puzzle_id_num trialNum
## <chr> <dbl> <chr> <fct> <dbl> <dbl>
## 1 3940-a6a959f6-… 23 Female Microba 67 0 1
## 2 3940-a6a959f6-… 23 Female Sokogen 13 3 2
## 3 3940-a6a959f6-… 23 Female Sokogen 32 6 3
## 4 3940-a6a959f6-… 23 Female Sokogen 18 9 4
## 5 3940-a6a959f6-… 23 Female Microba 104 12 5
## 6 3940-a6a959f6-… 23 Female Sokogen 38 15 6
## # ℹ 18 more variables: stimuli_set <chr>, layout <chr>,
## # select_response <dbl>, rating <dbl>, solveDuration <dbl>,
## # solved <dbl>, boxesSolved <dbl>, attempt_nInputEvents <dbl>,
## # attempt_nRestart <dbl>, attempt_nUndo <dbl>,
## # sokobanonline__solve_rate <dbl>, astar_iters <dbl>,
## # astar_solution_length <dbl>, judgedDifficulty <dbl>,
## # mean_difficult <dbl>, participantEffort <dbl>, …2 Descriptives
Age by condition:
df.analysis %>%
distinct(subject_id, age, .keep_all = F) %>%
summarise(n = n(),
M = mean(age),
SD = sd(age),
min = min(age),
max = max(age))## # A tibble: 1 × 5
## n M SD min max
## <int> <dbl> <dbl> <dbl> <dbl>
## 1 205 36.7 12.3 18 74Gender:
## # A tibble: 4 × 2
## gender n
## <chr> <int>
## 1 Female 87
## 2 Male 114
## 3 Non-binary 3
## 4 Prefer not to answer 1Experience:
## # A tibble: 4 × 2
## sokobanFamiliarity n
## <fct> <int>
## 1 Never 126
## 2 A few times 53
## 3 Several times 18
## 4 Very familiar 83 Plots
3.1 % solved per puzzle
df.analysis %>%
group_by(puzzle_id_sorted) %>%
summarise(n = n(),
M = mean(solved, na.rm = T),
SD = sd(solved, na.rm = T),
min = min(solved, na.rm = T),
max = max(solved, na.rm = T)) %>%
arrange(desc(M))## # A tibble: 24 × 6
## puzzle_id_sorted n M SD min max
## <fct> <int> <dbl> <dbl> <dbl> <dbl>
## 1 Dimitri 37 67 0.806 0.398 0 1
## 2 Sokogen 17 67 0.776 0.420 0 1
## 3 Microba 48 67 0.731 0.447 0 1
## 4 Microba 43 70 0.671 0.473 0 1
## 5 Sokogen 14 70 0.671 0.473 0 1
## 6 Sokogen 6 67 0.627 0.487 0 1
## 7 Microba 41 67 0.567 0.499 0 1
## 8 Sokogen 32 68 0.5 0.504 0 1
## 9 Sokogen 13 68 0.471 0.503 0 1
## 10 Microba 26 70 0.443 0.500 0 1
## # ℹ 14 more rowsdf.analysis %>%
filter(!is.na(solved)) %>%
mutate(puzzle_id_sorted = fct_reorder(puzzle_id_sorted,
solved,
.fun = mean, .na_rm = TRUE)) %>%
group_by(puzzle_id_sorted) %>%
filter(n() > 0) %>%
ungroup() %>%
ggplot(aes(x = factor(puzzle_id_sorted),
y = (solved)*100,
fill = stimuli_set)) +
stat_summary(fun = mean,
geom = "bar",
width = 0.6) +
stat_summary(fun.data = mean_cl_boot,
geom = "errorbar",
width = 0.2) +
scale_y_continuous(limits = c(0, 100),
breaks = seq(0, 100, 25)) +
labs(x = "Puzzle name",
y = "% solved",
title = "% solved per puzzle",
subtitle = "N = 205 subjects, 24 puzzles total (n = 67-70 each)",
fill = "Puzzle block") +
coord_flip()
3.2 No of boxes solved per puzzle
df.analysis %>%
group_by(puzzle_id_sorted) %>%
summarise(n = n(),
M = mean(boxesSolved, na.rm = T),
SD = sd(boxesSolved, na.rm = T),
min = min(boxesSolved, na.rm = T),
max = max(boxesSolved, na.rm = T)) %>%
arrange(desc(M))## # A tibble: 24 × 6
## puzzle_id_sorted n M SD min max
## <fct> <int> <dbl> <dbl> <dbl> <dbl>
## 1 Dimitri 37 67 2.78 0.487 1 3
## 2 Sokogen 17 67 2.64 0.711 1 3
## 3 Microba 43 70 2.57 0.672 1 3
## 4 Microba 48 67 2.52 0.859 0 3
## 5 Sokogen 6 67 2.51 0.726 0 3
## 6 Sokogen 14 70 2.49 0.812 0 3
## 7 Sokogen 32 68 2.41 0.674 0 3
## 8 Sokogen 13 68 2.40 0.626 1 3
## 9 Microba 41 67 2.36 0.811 1 3
## 10 Microba 17 70 2.33 0.557 0 3
## # ℹ 14 more rowsdf.analysis %>%
filter(!is.na(solved)) %>%
mutate(puzzle_id_sorted = fct_reorder(puzzle_id_sorted,
solved,
.fun = mean, .na_rm = TRUE)) %>%
group_by(puzzle_id_sorted) %>%
filter(n() > 0) %>%
ungroup() %>%
ggplot(aes(x = factor(puzzle_id_sorted),
y = boxesSolved)) +
stat_summary(fun.data = mean_cl_boot,
geom = "pointrange",
width = 0.2,
aes(color = stimuli_set)) +
geom_point(position = position_jitter(height = .05,
width = 0.1),
alpha = .05,
size = 2,
show.legend = FALSE) +
scale_y_continuous(limits = c(0, 3),
breaks = seq(0, 3, 1)) +
labs(x = "Puzzle name",
y = "# of boxes solved",
title = "Number of boxes solved per puzzle (out of 3)",
subtitle = "N = 205 subjects, 24 puzzles total (n = 67-70 each)",
color = "Puzzle block") +
coord_flip()
3.3 No of actions
df.analysis %>%
group_by(puzzle_id_sorted) %>%
summarise(n = n(),
M = mean(attempt_nInputEvents),
SD = sd(attempt_nInputEvents),
min = min(attempt_nInputEvents),
max = max(attempt_nInputEvents)) %>%
arrange(desc(M))## # A tibble: 24 × 6
## puzzle_id_sorted n M SD min max
## <fct> <int> <dbl> <dbl> <dbl> <dbl>
## 1 Microba 33 67 265. 129. 43 622
## 2 Sokogen 40 70 236. 139. 22 614
## 3 Microba 104 68 228. 144. 10 608
## 4 Microba 67 68 224. 110. 23 473
## 5 Sokogen 41 70 211. 121. 8 537
## 6 Sokogen 46 70 209. 121. 17 511
## 7 Sokogen 38 68 198. 109. 12 475
## 8 Sokogen 39 67 195. 109. 34 429
## 9 Sokogen 19 67 192. 105. 28 558
## 10 Microba 26 70 190. 126. 23 548
## # ℹ 14 more rowsdf.analysis %>%
filter(!is.na(solved)) %>%
mutate(puzzle_id_sorted = fct_reorder(puzzle_id_sorted,
solved,
.fun = mean, .na_rm = TRUE)) %>%
group_by(puzzle_id_sorted) %>%
filter(n() > 0) %>%
ungroup() %>%
ggplot(aes(x = factor(puzzle_id_sorted),
y = attempt_nInputEvents)) +
stat_summary(fun.data = mean_cl_boot,
geom = "pointrange",
width = 0.2,
aes(color = stimuli_set)) +
geom_point(position = position_jitter(height = .05,
width = .1),
alpha = .05,
size = 2,
show.legend = FALSE) +
scale_y_continuous(limits = c(0, 600),
breaks = seq(0, 600, 50)) +
labs(x = "Puzzle name",
y = "# of moves attempted",
title = "Number of moves per puzzle",
subtitle = "N = 205 subjects, 24 puzzles total (n = 67-70 each)",
color = "Puzzle block") +
coord_flip()
3.4 Time until solution
df.analysis %>%
group_by(puzzle_id_sorted) %>%
summarise(n = n(),
M = mean(solveDuration, na.rm = T),
SD = sd(solveDuration, na.rm = T),
min = min(solveDuration, na.rm = T),
max = max(solveDuration, na.rm = T)) %>%
arrange(desc(M))## # A tibble: 24 × 6
## puzzle_id_sorted n M SD min max
## <fct> <int> <dbl> <dbl> <dbl> <dbl>
## 1 Sokogen 46 70 248. 51.7 160 300
## 2 Microba 104 68 212. 57.5 156 280
## 3 Sokogen 35 68 204. 62.4 82 276
## 4 Sokogen 34 68 197. 58.4 103 299
## 5 Sokogen 40 70 191. 97.8 104 297
## 6 Microba 33 67 191. 82.8 39 295
## 7 Microba 41 67 185. 68.6 63 293
## 8 Sokogen 41 70 184. 64.7 95 297
## 9 Sokogen 39 67 182. 70.1 82 288
## 10 Sokogen 38 68 167. 58.6 81 221
## # ℹ 14 more rowsdf.analysis %>%
filter(!is.na(solved)) %>%
mutate(puzzle_id_sorted = fct_reorder(puzzle_id_sorted,
solved,
.fun = mean, .na_rm = TRUE)) %>%
group_by(puzzle_id_sorted) %>%
filter(n() > 0) %>%
ungroup() %>%
ggplot(aes(x = factor(puzzle_id_sorted),
y = solveDuration)) +
stat_summary(fun.data = mean_cl_boot,
geom = "pointrange",
width = 0.2,
aes(color = stimuli_set)) +
geom_point(position = position_jitter(height = .05,
width = .1),
size = 2,
alpha = .05,
show.legend = FALSE) +
scale_y_continuous(limits = c(0, 300),
breaks = seq(0, 300, 60)) +
labs(x = "Puzzle name",
y = "Time until solution (in sec)",
title = "Time until solution per puzzle",
subtitle = "N = 205 subjects, 24 puzzles total (n = 67-70 each)",
color = "Puzzle block") +
coord_flip()
4 Modeling
4.1 Improvement over time
4.1.1 Performance on first half of puzzles vs last half of puzzles
Do people generally become better at Sokoban over time?
I.e., do we see differences in performance metrics (% solved, boxes solved, time until solution, number of steps) when we compare the first four puzzles people solved, vs the last four puzzles people solved?
4.1.1.1 % solved
plot1 =
df.analysis %>%
mutate(trialNum = case_when(trialNum > 4 ~ "Last half of puzzles",
trialNum <= 4 ~ "First half of puzzles"),
puzzle_id_sorted = fct_reorder(puzzle_id_sorted,
solved,
.fun = mean, .na_rm = TRUE)) %>%
filter(!is.na(trialNum)) %>%
ggplot(aes(x = puzzle_id_sorted,
y = (solved)*100,
fill = trialNum)) +
stat_summary(fun = mean,
geom = "bar",
width = .6,
position = position_dodge(.8)) +
stat_summary(fun.data = mean_cl_boot,
geom = "errorbar",
position = position_dodge(.8)) +
scale_y_continuous(limits = c(0, 100),
breaks = seq(0, 100, 25)) +
labs(x = "Puzzle name",
y = "% solved",
title = "% solved over time",
fill = "Stage") +
coord_flip() +
theme(legend.position = "top")
plot1
Do we see a progression in % solved when we break it down by puzzle order?
df.analysis %>%
group_by(trialNum, puzzle_id_sorted) %>%
summarise(mean = mean(solved)) %>%
ggplot(aes(x = trialNum,
y = (mean*100),
color = puzzle_id_sorted)) +
geom_point(position = position_jitter(width = .1,
height = .1),
size = 2,
alpha = .4) +
labs(x = "Puzzle order (1 through 8)",
y = "% solved",
title = "% solved over time",
fill = "Puzzle") +
theme(legend.position = "none") +
scale_x_continuous(breaks = seq(1,8,1))
Fitting the mixed effects model:
# mixed effects model
lm.pct_solved_empty =
glmer(solved ~
1 +
# controlling for other variables
scale(age) + # age
scale(sokobanonline__solve_rate) + # difficulty
scale(astar_iters) + # difficulty
scale(participantEffort) + # subjective effort
# random intercept for player
(1 | subject_id),
family = binomial(link = "logit"),
data = df.analysis)
lm.pct_solved_order =
glmer(solved ~
1 +
# fixed effect for puzzle order
trialNum +
# controlling for other variables
scale(age) + # age
scale(sokobanonline__solve_rate) + # difficulty
scale(astar_iters) + # difficulty
scale(participantEffort) + # subjective effort
# random intercept for player
(1 | subject_id),
family = binomial(link = "logit"),
data = df.analysis)
# summary
lm.pct_solved_order %>%
summary()## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula:
## solved ~ 1 + trialNum + scale(age) + scale(sokobanonline__solve_rate) +
## scale(astar_iters) + scale(participantEffort) + (1 | subject_id)
## Data: df.analysis
##
## AIC BIC logLik deviance df.resid
## 1840.4 1878.2 -913.2 1826.4 1633
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0237 -0.5676 -0.3125 0.6583 3.3794
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject_id (Intercept) 1.835 1.355
## Number of obs: 1640, groups: subject_id, 205
##
## Fixed effects:
## Estimate Std. Error z value
## (Intercept) -0.392330 0.168491 -2.328
## trialNum -0.098816 0.027951 -3.535
## scale(age) -0.218847 0.117493 -1.863
## scale(sokobanonline__solve_rate) 0.824983 0.071831 11.485
## scale(astar_iters) 0.004801 0.063904 0.075
## scale(participantEffort) 0.117835 0.115586 1.019
## Pr(>|z|)
## (Intercept) 0.019886 *
## trialNum 0.000407 ***
## scale(age) 0.062514 .
## scale(sokobanonline__solve_rate) < 2e-16 ***
## scale(astar_iters) 0.940118
## scale(participantEffort) 0.307987
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trilNm scl(g) s(___) scl(_)
## trialNum -0.715
## scale(age) 0.015 0.017
## scl(skb___) 0.088 -0.241 -0.045
## scl(str_tr) 0.090 -0.133 -0.005 0.144
## scl(prtcpE) -0.007 -0.006 -0.118 0.024 0.004## Data: df.analysis
## Models:
## lm.pct_solved_empty: solved ~ 1 + scale(age) + scale(sokobanonline__solve_rate) + scale(astar_iters) + scale(participantEffort) + (1 | subject_id)
## lm.pct_solved_order: solved ~ 1 + trialNum + scale(age) + scale(sokobanonline__solve_rate) + scale(astar_iters) + scale(participantEffort) + (1 | subject_id)
## npar AIC BIC logLik deviance Chisq Df
## lm.pct_solved_empty 6 1851.1 1883.5 -919.54 1839.1
## lm.pct_solved_order 7 1840.4 1878.2 -913.20 1826.4 12.691 1
## Pr(>Chisq)
## lm.pct_solved_empty
## lm.pct_solved_order 0.0003674 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## $trialNum
## # Predicted probabilities of solved
##
## trialNum | Predicted | 95% CI
## ---------------------------------
## 1 | 0.47 | 0.48, 0.51
## 2 | 0.46 | 0.48, 0.51
## 3 | 0.46 | 0.48, 0.50
## 4 | 0.45 | 0.48, 0.50
## 5 | 0.43 | 0.47, 0.50
## 6 | 0.42 | 0.47, 0.50
## 7 | 0.41 | 0.46, 0.49
## 8 | 0.39 | 0.45, 0.49
##
## Adjusted for:
## * age = 36.74
## * sokobanonline__solve_rate = 0.73
## * astar_iters = 6796.94
## * participantEffort = 4.80
## * subject_id = 0 (population-level)
##
## $age
## # Predicted probabilities of solved
##
## age | Predicted | 95% CI
## ----------------------------
## 15 | 0.48 | 0.47, 0.52
## 20 | 0.47 | 0.47, 0.51
## 30 | 0.45 | 0.48, 0.50
## 40 | 0.43 | 0.47, 0.50
## 45 | 0.42 | 0.46, 0.50
## 50 | 0.41 | 0.45, 0.50
## 60 | 0.38 | 0.42, 0.50
## 75 | 0.34 | 0.35, 0.50
##
## Adjusted for:
## * trialNum = 4.50
## * sokobanonline__solve_rate = 0.73
## * astar_iters = 6796.94
## * participantEffort = 4.80
## * subject_id = 0 (population-level)##
## $sokobanonline__solve_rate
## # Predicted probabilities of solved
##
## sokobanonline__solve_rate | Predicted | 95% CI
## --------------------------------------------------
## 0.40 | 0.03 | 0.04, 0.14
## 0.60 | 0.21 | 0.31, 0.42
## 0.80 | 0.50 | 0.49, 0.51
## 1.00 | 0.76 | 0.54, 0.68
##
## Adjusted for:
## * trialNum = 4.50
## * age = 36.74
## * astar_iters = 6796.94
## * participantEffort = 4.80
## * subject_id = 0 (population-level)
##
## $astar_iters
## # Predicted probabilities of solved
##
## astar_iters | Predicted | 95% CI
## ------------------------------------
## 650 | 0.44 | 0.47, 0.50
## 5500 | 0.44 | 0.47, 0.50
## 10300 | 0.44 | 0.47, 0.50
## 15150 | 0.44 | 0.47, 0.50
## 20000 | 0.44 | 0.47, 0.50
## 24800 | 0.44 | 0.47, 0.50
## 29650 | 0.44 | 0.46, 0.51
## 39300 | 0.44 | 0.45, 0.51
##
## Adjusted for:
## * trialNum = 4.50
## * age = 36.74
## * sokobanonline__solve_rate = 0.73
## * participantEffort = 4.80
## * subject_id = 0 (population-level)##
## $participantEffort
## # Predicted probabilities of solved
##
## participantEffort | Predicted | 95% CI
## ------------------------------------------
## 1 | 0.30 | 0.17, 0.56
## 3 | 0.38 | 0.37, 0.52
## 4 | 0.42 | 0.45, 0.50
## 5 | 0.44 | 0.48, 0.50
##
## Adjusted for:
## * trialNum = 4.50
## * age = 36.74
## * sokobanonline__solve_rate = 0.73
## * astar_iters = 6796.94
## * subject_id = 0 (population-level)
##
## attr(,"class")
## [1] "ggalleffects" "list"
## attr(,"model.name")
## [1] "."4.1.1.2 Boxes solved
plot2 =
df.analysis %>%
mutate(trialNum = case_when(trialNum > 4 ~ "Last half of puzzles",
trialNum <= 4 ~ "First half of puzzles"),
puzzle_id_sorted = fct_reorder(puzzle_id_sorted,
solved,
.fun = mean, .na_rm = TRUE)) %>%
filter(!is.na(trialNum)) %>%
ggplot(aes(x = puzzle_id_sorted,
y = boxesSolved,
color = trialNum)) +
stat_summary(fun.data = mean_cl_boot,
geom = "pointrange",
position = position_dodge(.8)) +
geom_point(position = position_jitter(width = .1,
height = .1),
size = 2,
alpha = .1) +
scale_y_continuous(limits = c(0, 3),
breaks = seq(0,3,1)) +
labs(x = "Puzzle name",
y = "# of boxes solved (0-3)",
title = "# of boxes solved over time",
color = "Stage") +
coord_flip() +
theme(legend.position = "top")
plot2
When broken down by individual puzzle:
df.analysis %>%
group_by(trialNum, puzzle_id_sorted) %>%
summarise(mean = mean(boxesSolved)) %>%
ggplot(aes(x = trialNum,
y = mean,
color = puzzle_id_sorted)) +
geom_point(position = position_jitter(width = .1,
height = .1),
size = 2,
alpha = .4) +
labs(x = "Puzzle order (1 through 8)",
y = "Mean # of boxes solved",
title = "Mean # of boxes solved over time",
fill = "Puzzle") +
theme(legend.position = "none") +
scale_x_continuous(breaks = seq(1,8,1)) +
scale_y_continuous(limits = c(0,3),
breaks = seq(0,3,1))
Fitting the mixed effects model:
# mixed effects model
lm.number_solved_empty =
glmer(boxesSolved ~
1 +
# controlling for other variables
scale(age) + # age
scale(sokobanonline__solve_rate) + # difficulty
scale(astar_iters) + # difficulty
scale(participantEffort) + # subjective effort
# random intercept for player
(1 | subject_id),
family = poisson(link = "log"),
data = df.analysis)
lm.number_solved_order =
glmer(boxesSolved ~
1 +
# fixed effect for puzzle order (controlling for difficulty)
trialNum +
# controlling for other variables
scale(age) + # age
scale(sokobanonline__solve_rate) + # difficulty
scale(astar_iters) + # difficulty
scale(participantEffort) + # subjective effort
# random intercept for player
(1 | subject_id),
family = poisson(link = "log"),
data = df.analysis)
# summary
lm.number_solved_order %>%
summary()## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: poisson ( log )
## Formula:
## boxesSolved ~ 1 + trialNum + scale(age) + scale(sokobanonline__solve_rate) +
## scale(astar_iters) + scale(participantEffort) + (1 | subject_id)
## Data: df.analysis
##
## AIC BIC logLik deviance df.resid
## 4820.1 4857.9 -2403.1 4806.1 1633
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.57643 -0.25869 0.02915 0.48384 1.06362
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject_id (Intercept) 0 0
## Number of obs: 1640, groups: subject_id, 205
##
## Fixed effects:
## Estimate Std. Error z value
## (Intercept) 0.815209 0.037541 21.715
## trialNum -0.017653 0.007571 -2.332
## scale(age) -0.024591 0.017303 -1.421
## scale(sokobanonline__solve_rate) 0.087131 0.016979 5.132
## scale(astar_iters) -0.037730 0.018226 -2.070
## scale(participantEffort) 0.010122 0.017409 0.581
## Pr(>|z|)
## (Intercept) < 2e-16 ***
## trialNum 0.0197 *
## scale(age) 0.1553
## scale(sokobanonline__solve_rate) 2.87e-07 ***
## scale(astar_iters) 0.0384 *
## scale(participantEffort) 0.5610
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trilNm scl(g) s(___) scl(_)
## trialNum -0.890
## scale(age) 0.011 0.000
## scl(skb___) 0.092 -0.144 -0.005
## scl(str_tr) 0.127 -0.121 -0.004 0.106
## scl(prtcpE) -0.001 -0.004 -0.107 0.005 0.005
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')## Data: df.analysis
## Models:
## lm.number_solved_empty: boxesSolved ~ 1 + scale(age) + scale(sokobanonline__solve_rate) + scale(astar_iters) + scale(participantEffort) + (1 | subject_id)
## lm.number_solved_order: boxesSolved ~ 1 + trialNum + scale(age) + scale(sokobanonline__solve_rate) + scale(astar_iters) + scale(participantEffort) + (1 | subject_id)
## npar AIC BIC logLik deviance Chisq Df
## lm.number_solved_empty 6 4823.6 4856.0 -2405.8 4811.6
## lm.number_solved_order 7 4820.1 4857.9 -2403.1 4806.1 5.4415 1
## Pr(>Chisq)
## lm.number_solved_empty
## lm.number_solved_order 0.01966 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## $trialNum
## # Predicted counts of boxesSolved
##
## trialNum | Predicted | 95% CI
## ---------------------------------
## 1 | 2.22 | 2.09, 2.36
## 2 | 2.18 | 2.08, 2.29
## 3 | 2.14 | 2.06, 2.23
## 4 | 2.11 | 2.03, 2.18
## 5 | 2.07 | 2.00, 2.14
## 6 | 2.03 | 1.95, 2.12
## 7 | 2.00 | 1.90, 2.10
## 8 | 1.96 | 1.84, 2.09
##
## Adjusted for:
## * age = 36.74
## * sokobanonline__solve_rate = 0.73
## * astar_iters = 6796.94
## * participantEffort = 4.80
## * subject_id = 0 (population-level)
##
## $age
## # Predicted counts of boxesSolved
##
## age | Predicted | 95% CI
## ----------------------------
## 15 | 2.18 | 2.04, 2.33
## 20 | 2.16 | 2.04, 2.28
## 30 | 2.12 | 2.04, 2.20
## 40 | 2.07 | 2.00, 2.15
## 45 | 2.05 | 1.97, 2.14
## 50 | 2.03 | 1.93, 2.14
## 60 | 1.99 | 1.85, 2.14
## 75 | 1.93 | 1.73, 2.16
##
## Adjusted for:
## * trialNum = 4.50
## * sokobanonline__solve_rate = 0.73
## * astar_iters = 6796.94
## * participantEffort = 4.80
## * subject_id = 0 (population-level)##
## $sokobanonline__solve_rate
## # Predicted counts of boxesSolved
##
## sokobanonline__solve_rate | Predicted | 95% CI
## --------------------------------------------------
## 0.40 | 1.44 | 1.24, 1.67
## 0.60 | 1.80 | 1.68, 1.93
## 0.80 | 2.26 | 2.16, 2.36
## 1.00 | 2.83 | 2.51, 3.18
##
## Adjusted for:
## * trialNum = 4.50
## * age = 36.74
## * astar_iters = 6796.94
## * participantEffort = 4.80
## * subject_id = 0 (population-level)
##
## $astar_iters
## # Predicted counts of boxesSolved
##
## astar_iters | Predicted | 95% CI
## ------------------------------------
## 650 | 2.14 | 2.05, 2.22
## 5500 | 2.10 | 2.03, 2.17
## 10300 | 2.06 | 1.98, 2.14
## 15150 | 2.02 | 1.93, 2.12
## 20000 | 1.98 | 1.87, 2.11
## 24800 | 1.95 | 1.80, 2.10
## 29650 | 1.91 | 1.74, 2.09
## 39300 | 1.84 | 1.62, 2.09
##
## Adjusted for:
## * trialNum = 4.50
## * age = 36.74
## * sokobanonline__solve_rate = 0.73
## * participantEffort = 4.80
## * subject_id = 0 (population-level)##
## $participantEffort
## # Predicted counts of boxesSolved
##
## participantEffort | Predicted | 95% CI
## ------------------------------------------
## 1 | 1.94 | 1.50, 2.50
## 3 | 2.01 | 1.78, 2.28
## 4 | 2.05 | 1.93, 2.19
## 5 | 2.10 | 2.02, 2.17
##
## Adjusted for:
## * trialNum = 4.50
## * age = 36.74
## * sokobanonline__solve_rate = 0.73
## * astar_iters = 6796.94
## * subject_id = 0 (population-level)
##
## attr(,"class")
## [1] "ggalleffects" "list"
## attr(,"model.name")
## [1] "."4.1.1.3 Time spent
plot3 =
df.analysis %>%
mutate(trialNum = case_when(trialNum > 4 ~ "Last half of puzzles",
trialNum <= 4 ~ "First half of puzzles"),
puzzle_id_sorted = fct_reorder(puzzle_id_sorted,
solved,
.fun = mean, .na_rm = TRUE)) %>%
filter(!is.na(trialNum)) %>%
ggplot(aes(x = puzzle_id_sorted,
y = solveDuration,
color = trialNum)) +
stat_summary(fun.data = mean_cl_boot,
geom = "pointrange",
position = position_dodge(.8)) +
geom_point(position = position_jitter(width = .1,
height = .1),
size = 2,
alpha = .1) +
scale_y_continuous(limits = c(0, 300),
breaks = seq(0,300,60)) +
labs(x = "Puzzle name",
y = "# of boxes solved (0-3)",
title = "# of boxes solved over time",
color = "Stage") +
coord_flip() +
theme(legend.position = "top")
plot3
When broken down by puzzle:
df.analysis %>%
group_by(trialNum, puzzle_id_sorted) %>%
summarise(mean = mean(solveDuration, na.rm = T)) %>%
ggplot(aes(x = trialNum,
y = mean,
color = puzzle_id_sorted)) +
geom_point(position = position_jitter(width = .1,
height = .1),
size = 2,
alpha = .4) +
labs(x = "Puzzle order (1 through 8)",
y = "Mean solve time",
title = "Mean solve time over time",
fill = "Puzzle") +
theme(legend.position = "none") +
scale_x_continuous(breaks = seq(1,8,1)) +
scale_y_continuous(limits = c(0,300),
breaks = seq(0,300,60))
Fitting the mixed effects model:
# mixed effects model
lm.duration_order_empty =
glmer(solveDuration ~
1 +
# controlling for other variables
scale(age) + # age
scale(sokobanonline__solve_rate) + # difficulty
scale(astar_iters) + # difficulty
scale(participantEffort) + # subjective effort
# random intercept for player
(1 | subject_id),
family = poisson(link = "log"),
data = df.analysis)
lm.duration_order =
glmer(solveDuration ~
1 +
# fixed effect for puzzle order (controlling for difficulty)
trialNum +
# controlling for other variables
scale(age) + # age
scale(sokobanonline__solve_rate) + # difficulty
scale(astar_iters) + # difficulty
scale(participantEffort) + # subjective effort
# random intercept for player
(1 | subject_id),
family = poisson(link = "log"),
data = df.analysis)
# summary
lm.duration_order %>%
summary()## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: poisson ( log )
## Formula:
## solveDuration ~ 1 + trialNum + scale(age) + scale(sokobanonline__solve_rate) +
## scale(astar_iters) + scale(participantEffort) + (1 | subject_id)
## Data: df.analysis
##
## AIC BIC logLik deviance df.resid
## 19297.2 19327.9 -9641.6 19283.2 587
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -10.758 -3.800 -0.253 3.056 16.312
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject_id (Intercept) 0.1523 0.3903
## Number of obs: 594, groups: subject_id, 170
##
## Fixed effects:
## Estimate Std. Error z value
## (Intercept) 4.964997 0.031484 157.700
## trialNum 0.009484 0.001956 4.848
## scale(age) 0.022585 0.031470 0.718
## scale(sokobanonline__solve_rate) -0.126157 0.004136 -30.505
## scale(astar_iters) 0.026036 0.004693 5.547
## scale(participantEffort) 0.011174 0.030190 0.370
## Pr(>|z|)
## (Intercept) < 2e-16 ***
## trialNum 1.25e-06 ***
## scale(age) 0.473
## scale(sokobanonline__solve_rate) < 2e-16 ***
## scale(astar_iters) 2.90e-08 ***
## scale(participantEffort) 0.711
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trilNm scl(g) s(___) scl(_)
## trialNum -0.264
## scale(age) 0.073 -0.007
## scl(skb___) -0.022 -0.091 0.002
## scl(str_tr) 0.097 -0.356 0.005 0.098
## scl(prtcpE) -0.017 -0.001 -0.151 0.004 -0.006## Data: df.analysis
## Models:
## lm.duration_order_empty: solveDuration ~ 1 + scale(age) + scale(sokobanonline__solve_rate) + scale(astar_iters) + scale(participantEffort) + (1 | subject_id)
## lm.duration_order: solveDuration ~ 1 + trialNum + scale(age) + scale(sokobanonline__solve_rate) + scale(astar_iters) + scale(participantEffort) + (1 | subject_id)
## npar AIC BIC logLik deviance Chisq Df
## lm.duration_order_empty 6 19319 19345 -9653.3 19307
## lm.duration_order 7 19297 19328 -9641.6 19283 23.49 1
## Pr(>Chisq)
## lm.duration_order_empty
## lm.duration_order 1.256e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## $trialNum
## # Predicted counts of solveDuration
##
## trialNum | Predicted | 95% CI
## -------------------------------------
## 1 | 138.16 | 130.46, 147.28
## 2 | 139.48 | 131.79, 148.58
## 3 | 140.81 | 133.10, 149.93
## 4 | 142.15 | 134.40, 151.33
## 5 | 143.50 | 135.67, 152.78
## 6 | 144.87 | 136.92, 154.28
## 7 | 146.25 | 138.15, 155.84
## 8 | 147.64 | 139.36, 157.45
##
## Adjusted for:
## * age = 35.78
## * sokobanonline__solve_rate = 0.76
## * astar_iters = 6266.02
## * participantEffort = 4.83
## * subject_id = 0 (population-level)
##
## $age
## # Predicted counts of solveDuration
##
## age | Predicted | 95% CI
## --------------------------------
## 15 | 137.35 | 122.14, 155.47
## 20 | 138.62 | 125.89, 153.63
## 30 | 141.19 | 132.55, 151.37
## 40 | 143.81 | 135.51, 153.62
## 45 | 145.13 | 135.12, 156.91
## 50 | 146.47 | 134.01, 161.15
## 60 | 149.19 | 130.84, 171.24
## 75 | 153.36 | 125.36, 188.84
##
## Adjusted for:
## * trialNum = 4.41
## * sokobanonline__solve_rate = 0.76
## * astar_iters = 6266.02
## * participantEffort = 4.83
## * subject_id = 0 (population-level)##
## $sokobanonline__solve_rate
## # Predicted counts of solveDuration
##
## sokobanonline__solve_rate | Predicted | 95% CI
## ------------------------------------------------------
## 0.60 | 185.05 | 174.56, 197.45
## 0.70 | 157.19 | 148.58, 167.40
## 0.80 | 133.53 | 126.23, 142.18
## 0.90 | 113.43 | 107.05, 120.98
##
## Adjusted for:
## * trialNum = 4.41
## * age = 35.78
## * astar_iters = 6266.02
## * participantEffort = 4.83
## * subject_id = 0 (population-level)
##
## $astar_iters
## # Predicted counts of solveDuration
##
## astar_iters | Predicted | 95% CI
## ----------------------------------------
## 650 | 140.55 | 132.85, 149.67
## 5500 | 142.40 | 134.64, 151.60
## 10300 | 144.26 | 136.38, 153.59
## 15150 | 146.16 | 138.12, 155.69
## 20000 | 148.09 | 139.82, 157.87
## 24800 | 150.02 | 141.49, 160.11
## 29650 | 152.00 | 143.14, 162.46
## 39300 | 156.01 | 146.37, 167.37
##
## Adjusted for:
## * trialNum = 4.41
## * age = 35.78
## * sokobanonline__solve_rate = 0.76
## * participantEffort = 4.83
## * subject_id = 0 (population-level)##
## $participantEffort
## # Predicted counts of solveDuration
##
## participantEffort | Predicted | 95% CI
## ----------------------------------------------
## 1 | 131.31 | 84.68, 204.96
## 3 | 137.14 | 110.84, 170.80
## 4 | 140.16 | 125.94, 157.00
## 5 | 143.23 | 134.89, 153.09
##
## Adjusted for:
## * trialNum = 4.41
## * age = 35.78
## * sokobanonline__solve_rate = 0.76
## * astar_iters = 6266.02
## * subject_id = 0 (population-level)
##
## attr(,"class")
## [1] "ggalleffects" "list"
## attr(,"model.name")
## [1] "."4.1.1.4 No of moves
plot4 =
df.analysis %>%
mutate(trialNum = case_when(trialNum > 4 ~ "Last half of puzzles",
trialNum <= 4 ~ "First half of puzzles"),
puzzle_id_sorted = fct_reorder(puzzle_id_sorted,
solved,
.fun = mean, .na_rm = TRUE)) %>%
filter(!is.na(trialNum)) %>%
ggplot(aes(x = puzzle_id_sorted,
y = attempt_nInputEvents,
color = trialNum)) +
stat_summary(fun.data = mean_cl_boot,
geom = "pointrange",
position = position_dodge(.8)) +
geom_point(position = position_jitter(width = .1,
height = .1),
size = 2,
alpha = .1) +
labs(x = "Puzzle name",
y = "# of moves",
title = "# of moves over time",
color = "Stage") +
coord_flip() +
theme(legend.position = "top")
plot4
When broken down by puzzle:
df.analysis %>%
group_by(trialNum, puzzle_id_sorted) %>%
summarise(mean = mean(attempt_nInputEvents, na.rm = T)) %>%
ggplot(aes(x = trialNum,
y = mean,
color = puzzle_id_sorted)) +
geom_point(position = position_jitter(width = .1,
height = .1),
size = 2,
alpha = .4) +
labs(x = "Puzzle order (1 through 8)",
y = "Mean # of moves",
title = "Mean # of moves over time",
fill = "Puzzle") +
theme(legend.position = "none") +
scale_x_continuous(breaks = seq(1,8,1)) +
scale_y_continuous(limits = c(0, 600),
breaks = seq(0,600,100))
Fitting the mixed effects model:
# mixed effects model
lm.moves_order_empty =
glmer(attempt_nInputEvents ~
1 +
# controlling for other variables
scale(age) + # age
scale(sokobanonline__solve_rate) + # difficulty
scale(astar_iters) + # difficulty
scale(participantEffort) + # subjective effort
# random intercept for player
(1 | subject_id),
family = poisson(link = "log"),
data = df.analysis)
lm.moves_order =
glmer(attempt_nInputEvents ~
1 +
# fixed effect for puzzle order (controlling for difficulty)
trialNum +
# controlling for other variables
scale(age) + # age
scale(sokobanonline__solve_rate) + # difficulty
scale(astar_iters) + # difficulty
scale(participantEffort) + # subjective effort
# random intercept for player
(1 | subject_id),
family = poisson(link = "log"),
data = df.analysis)
# summary
lm.moves_order %>%
summary()## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: poisson ( log )
## Formula:
## attempt_nInputEvents ~ 1 + trialNum + scale(age) + scale(sokobanonline__solve_rate) +
## scale(astar_iters) + scale(participantEffort) + (1 | subject_id)
## Data: df.analysis
##
## AIC BIC logLik deviance df.resid
## 61033.1 61070.9 -30509.6 61019.1 1633
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -14.4090 -3.7989 -0.2077 3.2561 24.7126
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject_id (Intercept) 0.2083 0.4563
## Number of obs: 1640, groups: subject_id, 205
##
## Fixed effects:
## Estimate Std. Error z value
## (Intercept) 5.1546860 0.0321496 160.334
## trialNum -0.0206785 0.0008303 -24.904
## scale(age) -0.0645355 0.0321408 -2.008
## scale(sokobanonline__solve_rate) -0.1374895 0.0019654 -69.956
## scale(astar_iters) 0.0653442 0.0017487 37.366
## scale(participantEffort) -0.0589342 0.0321208 -1.835
## Pr(>|z|)
## (Intercept) <2e-16 ***
## trialNum <2e-16 ***
## scale(age) 0.0447 *
## scale(sokobanonline__solve_rate) <2e-16 ***
## scale(astar_iters) <2e-16 ***
## scale(participantEffort) 0.0665 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trilNm scl(g) s(___) scl(_)
## trialNum -0.114
## scale(age) 0.000 0.000
## scl(skb___) 0.029 -0.183 -0.001
## scl(str_tr) 0.010 -0.121 0.000 0.087
## scl(prtcpE) 0.000 0.000 -0.108 0.000 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## Model is nearly unidentifiable: very large eigenvalue
## - Rescale variables?## Data: df.analysis
## Models:
## lm.moves_order_empty: attempt_nInputEvents ~ 1 + scale(age) + scale(sokobanonline__solve_rate) + scale(astar_iters) + scale(participantEffort) + (1 | subject_id)
## lm.moves_order: attempt_nInputEvents ~ 1 + trialNum + scale(age) + scale(sokobanonline__solve_rate) + scale(astar_iters) + scale(participantEffort) + (1 | subject_id)
## npar AIC BIC logLik deviance Chisq Df
## lm.moves_order_empty 6 61651 61684 -30820 61639
## lm.moves_order 7 61033 61071 -30510 61019 620.3 1
## Pr(>Chisq)
## lm.moves_order_empty
## lm.moves_order < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## $trialNum
## # Predicted counts of attempt_nInputEvents
##
## trialNum | Predicted | 95% CI
## -------------------------------------
## 1 | 170.17 | 160.25, 181.71
## 2 | 166.69 | 156.99, 177.97
## 3 | 163.28 | 153.79, 174.32
## 4 | 159.93 | 150.65, 170.74
## 5 | 156.66 | 147.56, 167.25
## 6 | 153.45 | 144.54, 163.83
## 7 | 150.31 | 141.57, 160.50
## 8 | 147.24 | 138.65, 157.23
##
## Adjusted for:
## * age = 36.74
## * sokobanonline__solve_rate = 0.73
## * astar_iters = 6796.94
## * participantEffort = 4.80
## * subject_id = 0 (population-level)
##
## $age
## # Predicted counts of attempt_nInputEvents
##
## age | Predicted | 95% CI
## --------------------------------
## 15 | 177.43 | 156.58, 202.18
## 20 | 172.83 | 155.85, 192.73
## 30 | 163.99 | 153.10, 176.63
## 40 | 155.60 | 146.24, 166.48
## 45 | 151.57 | 140.93, 163.93
## 50 | 147.64 | 134.98, 162.39
## 60 | 140.09 | 122.78, 160.73
## 75 | 129.48 | 105.68, 159.52
##
## Adjusted for:
## * trialNum = 4.50
## * sokobanonline__solve_rate = 0.73
## * astar_iters = 6796.94
## * participantEffort = 4.80
## * subject_id = 0 (population-level)##
## $sokobanonline__solve_rate
## # Predicted counts of attempt_nInputEvents
##
## sokobanonline__solve_rate | Predicted | 95% CI
## ------------------------------------------------------
## 0.40 | 284.99 | 267.90, 304.86
## 0.60 | 199.71 | 188.06, 213.27
## 0.80 | 139.95 | 131.81, 149.43
## 1.00 | 98.07 | 92.24, 104.86
##
## Adjusted for:
## * trialNum = 4.50
## * age = 36.74
## * astar_iters = 6796.94
## * participantEffort = 4.80
## * subject_id = 0 (population-level)
##
## $astar_iters
## # Predicted counts of attempt_nInputEvents
##
## astar_iters | Predicted | 95% CI
## ----------------------------------------
## 650 | 151.83 | 143.01, 162.10
## 5500 | 156.90 | 147.79, 167.51
## 10300 | 162.09 | 152.68, 173.05
## 15150 | 167.51 | 157.77, 178.84
## 20000 | 173.11 | 163.03, 184.83
## 24800 | 178.83 | 168.40, 190.97
## 29650 | 184.81 | 173.99, 197.39
## 39300 | 197.30 | 185.65, 210.84
##
## Adjusted for:
## * trialNum = 4.50
## * age = 36.74
## * sokobanonline__solve_rate = 0.73
## * participantEffort = 4.80
## * subject_id = 0 (population-level)##
## $participantEffort
## # Predicted counts of attempt_nInputEvents
##
## participantEffort | Predicted | 95% CI
## ----------------------------------------------
## 1 | 244.79 | 153.44, 392.73
## 3 | 194.66 | 155.15, 245.59
## 4 | 173.58 | 154.89, 195.62
## 5 | 154.79 | 145.16, 165.98
##
## Adjusted for:
## * trialNum = 4.50
## * age = 36.74
## * sokobanonline__solve_rate = 0.73
## * astar_iters = 6796.94
## * subject_id = 0 (population-level)
##
## attr(,"class")
## [1] "ggalleffects" "list"
## attr(,"model.name")
## [1] "."4.2 Success on preceding puzzle
Does success on the previous puzzle influence specific puzzle choice?
df.analysis =
df.analysis %>%
mutate(prev_puzzle_solved = lag(solved))
df.analysis %>%
filter(!is.na(prev_puzzle_solved)) %>%
mutate(puzzle_id_ordered = fct_reorder(puzzle_id_sorted, sokobanonline__solve_rate),
prev_puzzle_solved = case_when(prev_puzzle_solved == 1 ~ "Yes",
prev_puzzle_solved == 0 ~ "No")) %>%
group_by(prev_puzzle_solved, stimuli_set, puzzle_id_sorted) %>%
summarise(n = n(), .groups = "drop") %>%
group_by(prev_puzzle_solved, stimuli_set) %>%
mutate(prop = n / sum(n)) %>%
ggplot(aes(x = factor(prev_puzzle_solved),
y = (prop*100),
fill = puzzle_id_sorted)) +
geom_col(position = "dodge") +
facet_wrap(~ stimuli_set + puzzle_id_sorted, ncol = 8) +
labs(x = "Previous puzzle solved?",
y = "% of times puzzle was chosen",
fill = "Puzzle",
title = "Player Puzzle Selection by Previous Puzzle Success") +
theme(legend.position = "none")
df.analysis %>%
mutate(puzzle_id_sorted = fct_reorder(puzzle_id_sorted,
solved,
.fun = mean, .na_rm = TRUE),
prev_puzzle_solved = case_when(prev_puzzle_solved == 1 ~ "Yes",
prev_puzzle_solved == 0 ~ "No")) %>%
filter(!is.na(prev_puzzle_solved)) %>%
ggplot(aes(x = puzzle_id_sorted,
y = (solved * 100),
fill = factor(prev_puzzle_solved))) +
stat_summary(fun = mean,
geom = "bar",
width = .6,
alpha = .5,
position = position_dodge(.8)) +
stat_summary(fun.data = mean_cl_boot,
geom = "errorbar",
position = position_dodge(.8)) +
scale_fill_manual(values = c("Yes" = "darkgreen",
"No" = "darkred")) +
labs(x = "Puzzle name",
y = "% solved",
fill = "Last puzzle solved?",
title = "% solved by previous puzzle success",
subtitle = "N = 205 subjects, 24 puzzles total (n = 67-70 each)") +
coord_flip() +
theme(legend.position = "right")
Fitting the mixed effects model:
# mixed effects model
df.subset = df.analysis %>%
filter(!is.na(prev_puzzle_solved),
!is.na(sokobanonline__solve_rate),
!is.na(participantEffort))
lm.reduced =
glmer(solved ~
1 +
scale(sokobanonline__solve_rate) +
scale(participantEffort) +
(1 | subject_id),
family = poisson(link = "log"),
data = df.subset)
lm.previous_performance =
glmer(solved ~
1 +
# fixed effect for previous puzzle solved
prev_puzzle_solved +
# controlling for other variables
scale(sokobanonline__solve_rate) + # difficulty
scale(participantEffort) + # subjective effort
# random intercept for player
(1 | subject_id),
family = poisson(link = "log"),
data = df.subset)
anova(lm.reduced, lm.previous_performance, test = "Chisq")## Data: df.subset
## Models:
## lm.reduced: solved ~ 1 + scale(sokobanonline__solve_rate) + scale(participantEffort) + (1 | subject_id)
## lm.previous_performance: solved ~ 1 + prev_puzzle_solved + scale(sokobanonline__solve_rate) + scale(participantEffort) + (1 | subject_id)
## npar AIC BIC logLik deviance Chisq Df
## lm.reduced 4 2294.8 2316.4 -1143.4 2286.8
## lm.previous_performance 5 2282.4 2309.5 -1136.2 2272.4 14.39 1
## Pr(>Chisq)
## lm.reduced
## lm.previous_performance 0.0001486 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: poisson ( log )
## Formula:
## solved ~ 1 + prev_puzzle_solved + scale(sokobanonline__solve_rate) +
## scale(participantEffort) + (1 | subject_id)
## Data: df.subset
##
## AIC BIC logLik deviance df.resid
## 2282.5 2309.5 -1136.2 2272.5 1634
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -0.8948 -0.5286 -0.4356 0.6578 2.2635
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject_id (Intercept) 0.1656 0.407
## Number of obs: 1639, groups: subject_id, 205
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.30400 0.06778 -19.238 < 2e-16
## prev_puzzle_solved 0.33470 0.08726 3.836 0.000125
## scale(sokobanonline__solve_rate) 0.35504 0.03951 8.985 < 2e-16
## scale(participantEffort) 0.04056 0.05201 0.780 0.435429
##
## (Intercept) ***
## prev_puzzle_solved ***
## scale(sokobanonline__solve_rate) ***
## scale(participantEffort)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) prv_p_ s(___)
## prv_pzzl_sl -0.502
## scl(skb___) -0.226 0.048
## scl(prtcpE) -0.014 -0.022 -0.007## $prev_puzzle_solved
## # Predicted counts of solved
##
## prev_puzzle_solved | Predicted | 95% CI
## -------------------------------------------
## 0 | 0.45 | 0.66, 0.85
## 1 | 0.63 | 0.91, 1.21
##
## Adjusted for:
## * sokobanonline__solve_rate = 0.73
## * participantEffort = 4.80
## * subject_id = 0 (population-level)
##
## $sokobanonline__solve_rate
## # Predicted counts of solved
##
## sokobanonline__solve_rate | Predicted | 95% CI
## --------------------------------------------------
## 0.40 | 0.11 | 0.13, 0.27
## 0.60 | 0.28 | 0.38, 0.56
## 0.80 | 0.70 | 1.04, 1.30
## 1.00 | 1.75 | 2.24, 3.80
##
## Adjusted for:
## * prev_puzzle_solved = 0.36
## * participantEffort = 4.80
## * subject_id = 0 (population-level)
##
## $participantEffort
## # Predicted counts of solved
##
## participantEffort | Predicted | 95% CI
## ------------------------------------------
## 1 | 0.38 | 0.29, 1.35
## 3 | 0.44 | 0.50, 1.07
## 4 | 0.48 | 0.65, 0.96
## 5 | 0.52 | 0.77, 0.96
##
## Adjusted for:
## * prev_puzzle_solved = 0.36
## * sokobanonline__solve_rate = 0.73
## * subject_id = 0 (population-level)
##
## attr(,"class")
## [1] "ggalleffects" "list"
## attr(,"model.name")
## [1] "."4.3 Growth curve model
% solved:
# null model: no learning over time
lm.solve_growth_null =
glmer(solved ~
1 +
# control vars
scale(age) + # age
scale(participantEffort) + # subjective effort
(1 | puzzle_id_sorted) + # random slope for puzzle
(1 + trialNum | subject_id), # random slopes and intercepts per subject
data = df.analysis,
family = binomial(link = "logit"),
control = glmerControl(optimizer = "bobyqa"))
lm.solve_growth =
glmer(solved ~
1 +
# fixed effect
trialNum +
# control vars
scale(age) + # age
scale(participantEffort) + # subjective effort
(1 | puzzle_id_sorted) + # random slope for puzzle
(1 + trialNum | subject_id), # random slopes and intercepts per subject
data = df.analysis,
family = binomial(link = "logit"),
control = glmerControl(optimizer = "bobyqa"))
lm.solve_growth %>%
summary()## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula:
## solved ~ 1 + trialNum + scale(age) + scale(participantEffort) +
## (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## Data: df.analysis
## Control: glmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 1544.0 1587.2 -764.0 1528.0 1632
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.3715 -0.4343 -0.1516 0.3906 8.6867
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## subject_id (Intercept) 1.77503 1.3323
## trialNum 0.01016 0.1008 1.00
## puzzle_id_sorted (Intercept) 4.25909 2.0638
## Number of obs: 1640, groups: subject_id, 205; puzzle_id_sorted, 24
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.183170 0.476426 -2.483 0.0130 *
## trialNum -0.008627 0.041586 -0.207 0.8357
## scale(age) -0.304039 0.143353 -2.121 0.0339 *
## scale(participantEffort) 0.136793 0.141100 0.969 0.3323
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trilNm scl(g)
## trialNum -0.340
## scale(age) 0.015 -0.012
## scl(prtcpE) -0.006 0.012 -0.119
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')## Data: df.analysis
## Models:
## lm.solve_growth_null: solved ~ 1 + scale(age) + scale(participantEffort) + (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## lm.solve_growth: solved ~ 1 + trialNum + scale(age) + scale(participantEffort) + (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## npar AIC BIC logLik deviance Chisq Df
## lm.solve_growth_null 7 1542 1579.9 -764.02 1528
## lm.solve_growth 8 1544 1587.2 -764.00 1528 0.043 1
## Pr(>Chisq)
## lm.solve_growth_null
## lm.solve_growth 0.8357df.analysis$predicted_solve =
predict(lm.solve_growth, type = "response")
df.analysis_subject =
df.analysis %>%
group_by(subject_id, trialNum) %>%
summarise(mean_pred = mean(predicted_solve, na.rm = TRUE),
.groups = "drop")
plot1 =
df.analysis_subject %>%
ggplot(aes(x = trialNum,
y = (mean_pred*100))) +
geom_line(aes(group = subject_id),
alpha = 0.1, color = "gray") + # individual trajectories
stat_summary(fun = mean,
geom = "line",
size = 1,
color = "#1f77b4") + # average curve
stat_summary(fun.data = mean_cl_boot,
geom = "ribbon",
aes(group = 1),
fill = "#1f77b4",
alpha = 0.2) +
labs(x = "Puzzle #",
y = "% solved",
title = "Predicted performance curves across puzzles: % solved",
subtitle = "Grey lines are predicted lines for individual subjects,\nblue line and ribbon equal predicted mean + 95% CI") +
scale_x_continuous(limits = c(1, 8),
breaks = seq(1,8,1)) +
theme_minimal()
plot1
boxes solved:
# null model: no learning over time
lm.boxes_growth_null =
glmer(boxesSolved ~
1 +
# control vars
scale(age) + # age
scale(participantEffort) + # subjective effort
(1 | puzzle_id_sorted) + # random slope for puzzle
(1 + trialNum | subject_id), # random slopes and intercepts per subject
data = df.analysis,
family = poisson(link = "log"),
control = glmerControl(optimizer = "bobyqa"))# full model:
lm.boxes_growth =
glmer(boxesSolved ~
1 +
trialNum +
# control vars
scale(age) + # age
scale(participantEffort) + # subjective effort
(1 | puzzle_id_sorted) + # random slope for puzzle
(1 + trialNum | subject_id), # random slopes and intercepts per subject
data = df.analysis,
family = poisson(link = "log"),
control = glmerControl(optimizer = "bobyqa"))
lm.boxes_growth %>%
summary()## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: poisson ( log )
## Formula:
## boxesSolved ~ 1 + trialNum + scale(age) + scale(participantEffort) +
## (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## Data: df.analysis
## Control: glmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 4759.0 4802.2 -2371.5 4743.0 1632
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.58261 -0.24194 -0.00553 0.33846 1.62867
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## subject_id (Intercept) 0.000e+00 0.000e+00
## trialNum 4.501e-16 2.122e-08 NaN
## puzzle_id_sorted (Intercept) 5.070e-02 2.252e-01
## Number of obs: 1640, groups: subject_id, 205; puzzle_id_sorted, 24
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.727597 0.063852 11.395 <2e-16 ***
## trialNum -0.002063 0.009041 -0.228 0.820
## scale(age) -0.025980 0.017257 -1.505 0.132
## scale(participantEffort) 0.008482 0.017548 0.483 0.629
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trilNm scl(g)
## trialNum -0.638
## scale(age) 0.008 -0.002
## scl(prtcpE) 0.001 -0.005 -0.112
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')## Data: df.analysis
## Models:
## lm.boxes_growth_null: boxesSolved ~ 1 + scale(age) + scale(participantEffort) + (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## lm.boxes_growth: boxesSolved ~ 1 + trialNum + scale(age) + scale(participantEffort) + (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## npar AIC BIC logLik deviance Chisq Df
## lm.boxes_growth_null 7 4757 4794.8 -2371.5 4743
## lm.boxes_growth 8 4759 4802.2 -2371.5 4743 0.0519 1
## Pr(>Chisq)
## lm.boxes_growth_null
## lm.boxes_growth 0.8199df.analysis$predicted_boxes =
predict(lm.boxes_growth, type = "response")
df.analysis_subject =
df.analysis %>%
group_by(subject_id, trialNum) %>%
summarise(mean_pred = mean(predicted_boxes, na.rm = TRUE),
.groups = "drop")
plot2 =
df.analysis_subject %>%
ggplot(aes(x = trialNum,
y = mean_pred)) +
geom_line(aes(group = subject_id),
alpha = 0.1, color = "gray") + # individual trajectories
stat_summary(fun = mean,
geom = "line",
size = 1,
color = "#1f77b4") + # average curve
stat_summary(fun = "errorbar",
geom = "line",
size = 1,
color = "#1f77b4") + # average curve
stat_summary(fun.data = mean_cl_boot,
geom = "ribbon",
aes(group = 1),
fill = "#1f77b4",
alpha = 0.2) +
labs(x = "Puzzle #",
y = "# of boxes solved",
title = "Predicted performance curves across puzzles: # of boxes solved",
subtitle = "Grey lines are predicted lines for individual subjects,\nblue line and ribbon equal predicted mean + 95% CI") +
scale_x_continuous(limits = c(1, 8),
breaks = seq(1,8,1)) +
scale_y_continuous(limits = c(0, 3),
breaks = seq(0,3, 1)) +
theme_minimal()
plot2
time to solution:
# null model: no learning over time
lm.time_growth_null =
glmer(solveDuration ~
1 +
# control vars
scale(age) + # age
scale(participantEffort) + # subjective effort
(1 | puzzle_id_sorted) + # random slope for puzzle
(1 + trialNum | subject_id), # random slopes and intercepts per subject
data = df.analysis,
family = poisson(link = "log"),
control = glmerControl(optimizer = "bobyqa"))# full model:
lm.time_growth =
glmer(solveDuration ~
1 +
trialNum +
# control vars
scale(age) + # age
scale(participantEffort) + # subjective effort
(1 | puzzle_id_sorted) + # random slope for puzzle
(1 + trialNum | subject_id), # random slopes and intercepts per subject
data = df.analysis,
family = poisson(link = "log"),
control = glmerControl(optimizer = "bobyqa"))
lm.time_growth %>%
summary()## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: poisson ( log )
## Formula:
## solveDuration ~ 1 + trialNum + scale(age) + scale(participantEffort) +
## (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## Data: df.analysis
## Control: glmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 13095.4 13130.5 -6539.7 13079.4 586
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -9.7278 -2.2725 -0.0664 1.6040 12.9123
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## subject_id (Intercept) 0.83535 0.9140
## trialNum 0.03517 0.1875 -0.87
## puzzle_id_sorted (Intercept) 0.11106 0.3333
## Number of obs: 594, groups: subject_id, 170; puzzle_id_sorted, 23
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 5.246034 0.102840 51.011 <2e-16 ***
## trialNum -0.040481 0.015905 -2.545 0.0109 *
## scale(age) 0.005152 0.038299 0.135 0.8930
## scale(participantEffort) 0.021529 0.035807 0.601 0.5477
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trilNm scl(g)
## trialNum -0.643
## scale(age) 0.023 0.000
## scl(prtcpE) 0.007 -0.005 -0.152## Data: df.analysis
## Models:
## lm.time_growth_null: solveDuration ~ 1 + scale(age) + scale(participantEffort) + (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## lm.time_growth: solveDuration ~ 1 + trialNum + scale(age) + scale(participantEffort) + (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## npar AIC BIC logLik deviance Chisq Df
## lm.time_growth_null 7 13100 13130 -6542.9 13086
## lm.time_growth 8 13095 13130 -6539.7 13079 6.424 1
## Pr(>Chisq)
## lm.time_growth_null
## lm.time_growth 0.01126 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1df.analysis =
df.analysis %>%
mutate(predicted_time = NA_real_)
df.analysis$predicted_time[df.analysis$solved == 1] =
predict(lm.time_growth, type = "response")
df.analysis_subject =
df.analysis %>%
group_by(subject_id, trialNum) %>%
summarise(mean_pred = mean(predicted_time, na.rm = TRUE),
.groups = "drop")
plot3 =
df.analysis_subject %>%
ggplot(aes(x = trialNum,
y = mean_pred)) +
geom_line(aes(group = subject_id),
alpha = 0.1, color = "gray") + # individual trajectories
stat_summary(fun = mean,
geom = "line",
size = 1,
color = "#1f77b4") + # average curve
stat_summary(fun = "errorbar",
geom = "line",
size = 1,
color = "#1f77b4") + # average curve
stat_summary(fun.data = mean_cl_boot,
geom = "ribbon",
aes(group = 1),
fill = "#1f77b4",
alpha = 0.2) +
labs(x = "Puzzle #",
y = "Time until solution",
title = "Predicted performance curves across puzzles: time until solution",
subtitle = "Grey lines are predicted lines for individual subjects,\nblue line and ribbon equal predicted mean + 95% CI") +
scale_x_continuous(limits = c(1, 8),
breaks = seq(1,8,1)) +
scale_y_continuous(limits = c(0, 300),
breaks = seq(0, 300, 60)) +
theme_minimal()
plot3
number of moves:
# null model: no learning over time
lm.moves_growth_null =
glmer(attempt_nInputEvents ~
1 +
# control vars
scale(age) + # age
scale(participantEffort) + # subjective effort
(1 | puzzle_id_sorted) + # random slope for puzzle
(1 + trialNum | subject_id), # random slopes and intercepts per subject
data = df.analysis,
family = poisson(link = "log"),
control = glmerControl(optimizer = "bobyqa"))# full model:
lm.moves_growth =
glmer(attempt_nInputEvents ~
1 +
trialNum +
# control vars
scale(age) + # age
scale(participantEffort) + # subjective effort
(1 | puzzle_id_sorted) + # random slope for puzzle
(1 + trialNum | subject_id), # random slopes and intercepts per subject
data = df.analysis,
family = poisson(link = "log"),
control = glmerControl(optimizer = "bobyqa"))
lm.moves_growth %>%
summary()## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: poisson ( log )
## Formula:
## attempt_nInputEvents ~ 1 + trialNum + scale(age) + scale(participantEffort) +
## (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## Data: df.analysis
## Control: glmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 44561.1 44604.4 -22272.6 44545.1 1632
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -14.8539 -2.8979 -0.1722 2.5324 21.2875
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## subject_id (Intercept) 0.26276 0.51260
## trialNum 0.00760 0.08718 -0.47
## puzzle_id_sorted (Intercept) 0.05728 0.23934
## Number of obs: 1640, groups: subject_id, 205; puzzle_id_sorted, 24
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 5.263712 0.060814 86.554 <2e-16 ***
## trialNum -0.053089 0.006198 -8.565 <2e-16 ***
## scale(age) -0.075497 0.032157 -2.348 0.0189 *
## scale(participantEffort) -0.062008 0.031997 -1.938 0.0526 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trilNm scl(g)
## trialNum -0.287
## scale(age) -0.001 0.001
## scl(prtcpE) 0.000 0.000 -0.108## Data: df.analysis
## Models:
## lm.moves_growth_null: attempt_nInputEvents ~ 1 + scale(age) + scale(participantEffort) + (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## lm.moves_growth: attempt_nInputEvents ~ 1 + trialNum + scale(age) + scale(participantEffort) + (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## npar AIC BIC logLik deviance Chisq Df
## lm.moves_growth_null 7 44622 44660 -22304 44608
## lm.moves_growth 8 44561 44604 -22273 44545 62.922 1
## Pr(>Chisq)
## lm.moves_growth_null
## lm.moves_growth 2.15e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1df.analysis$predicted_moves =
predict(lm.moves_growth, type = "response")
df.analysis_subject =
df.analysis %>%
group_by(subject_id, trialNum) %>%
summarise(mean_pred = mean(predicted_moves, na.rm = TRUE),
.groups = "drop")
plot4 =
df.analysis_subject %>%
ggplot(aes(x = trialNum,
y = mean_pred)) +
geom_line(aes(group = subject_id),
alpha = 0.1, color = "gray") + # individual trajectories
stat_summary(fun = mean,
geom = "line",
size = 1,
color = "#1f77b4") + # average curve
stat_summary(fun = "errorbar",
geom = "line",
size = 1,
color = "#1f77b4") + # average curve
stat_summary(fun.data = mean_cl_boot,
geom = "ribbon",
aes(group = 1),
fill = "#1f77b4",
alpha = 0.2) +
labs(x = "Puzzle #",
y = "# of moves",
title = "Predicted performance curves across puzzles: # of moves",
subtitle = "Grey lines are predicted lines for individual subjects,\nblue line and ribbon equal predicted mean + 95% CI") +
scale_x_continuous(limits = c(1, 8),
breaks = seq(1,8,1)) +
scale_y_continuous(limits = c(0, 600),
breaks = seq(0, 600, 100)) +
theme_minimal()
plot4
